Question: Subtract $-7a^2+3a-9$ from $5a^2-6a-4$.
Answer: Since we are asked to subtract $-7a^2+3a-9$ from $5a^2-6a-4$, let's rewrite it as one expression. But how do we know which terms go where? Well, if we were asked to "subtract $4$ from $9$ ", we would rewrite it as $9 - 4$. In other words, we would start with $9$ and then subtract $4$. Let's use this pattern to rewrite the problem as one expression: ${(5a^2-6a-4)-(-7a^2+3a-9)}$ Since we are subtracting, it is helpful to distribute the $\text{{negative sign}}$ across all terms in the second trinomial: $\begin{aligned}&(5a^2-6a-4){-}(-7a^2+3a-9)\\ \\ =&(5a^2-6a-4){-}(-7a^2){-}3a{-}(-9)\\ \\ =&5a^2-6a-4+7a^2-3a+9 \end{aligned}$ Note that the parentheses around the first trinomial don't affect the order of operations, so we can just remove them. When we add or subtract terms in a polynomial expression, the only way that we can simplify the expression is by combining those terms that are alike. Our expression contains terms of $3$ different degrees in the same variable: ${a^2}, {a},$ and the $\text{{constant}}$ term: ${{5a^2} {-6a} {-4} {+7a^2} {-3a} {+9}}$ Now that we have identified like terms, let's combine them. Make sure to keep track of positive and negative signs! ${{(5+7)a^2} + {(-6-3)a} + {(-4+9)}}$ When we combine the coefficients in front of each term, we get the following trinomial: $12a^2 -9a+5$